Tennessee v. Garner
Google up and read the above SCOUS case as applies to the police. Note the very restrictive guidelines pronounced. A lot of borderline areas can be in play depending on "the totality of the circumstances" to be Monday morning quarterbacked by others - police, prosecutors, jurors. I would say justifying shooting a fleeing felon as a private citizen would be at least as difficult as it would for the police.
I can say that we are trained to first be a good witness if off duty in plain clothes where a robbery goes down and the robber is just going to take the loot and run. We are probably not wearing a vest, may carry a smaller gun and less ammo than on duty, have no radio to call for back-up or maintain communication, and are not immediately visually recognizable as police when giving commands. Plus, in an exchange of gunfire innocent bystanders can get shot.
Some cues to engage would be if the robber discharges their weapon ( even into the ceiling or floor), herds people toward the back to a freezer locker or bathroom area, has people kneel or lay in an execution position, or covers peoples head with a blindfold, sack or whatever.
PS. Ever notice how police choose where and how to sit when eating at a restaurant?